Research
I work in Number Theory. More specifically, my main interst lies in Arithmetic Geometry,
where I work on Elliptic curves, Drinfeld modules, Drinfeld modular forms
and related topics.
Other interests include Ducci sequences, orders of elements in finte fields and most recently
quadratic number fields and the Cohen-Lenstra-Martinet heuristics.
Publications
Note: for copyright reasons, some of the following PDF files are not the final,
published versions. Also, this is page is under contruction, so most links are still
broken.
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Drinfeld modular polynomials of level T
(with Mahefason Heriniaina Razafinjatovo).
[ arXiv:2412.11324]
[GitHub]
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Heights of Drinfeld modular polynomials and Hecke images
(with Fabien Pazuki and Zhenlin Ran).
[ arXiv:2410.11132]
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Parity bias in fundamental units of real quadratic fields.
(with Cameron Shaw-Carmody), Bull. Aust. Math. Soc., to appear.
[PDF]
[GitHub]
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SeCritMass: Threshold Secret Petitions.
arXiv:2408.01255 [cs.CR]
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Explicit bounds on the coefficients of modular polynomials and the size of X0(N).
(with Fabien Pazuki and
Desirée Gijón Gómez)
Proc. London Math. Soc., to appear.
[PDF]
[GitHub]
- Explicit bounds on the coefficients of modular polynomials for the elliptic j-invariant.
(with Fabien Pazuki)
Proc. Amer. Math. Soc. Ser. B 11 (2024), 277–286.
[PDF]
- Drinfeld modular forms of arbitrary rank
(With Dirk Basson and
Richard Pink).
[PDF].
Mem. Amer. Math. Soc.
304 (2024) no. 1531, 94 pages.
[Published version].
This monograph updates (e.g. Prop 5.16) and combines the three preprints:
- Multiplicative orders of Gauss periods and the arithmetic of real
quadratic fields. Finite Fields Appl., 73 (2021).
[PDF]
arXiv:2006.10344
- Generic monodromy of Drinfeld modular varieties in special characteristic.
(With
Gebhard Böckle)
In: "Abelian Varieties and Number Theory" (M. Jarden, T. Shaska, eds.)
Contemp. Math., Amer. Math. Soc. 767, (2021), 147--160.
[PDF]
arXiv:1912.09820
- Heights and isogenies of Drinfeld modules.
(With Fabien Pazuki
and Heriniaina Razafinjatovo)
Acta Arith. 197 no.2 (2021), 111-128.
arXiv:1908.03485
[PDF]
- Lower bounds for periods of Ducci sequences.
(With Igor Shparlinski)
Bull. Aust. Math. Soc. 102 no.1 (2020), 31-38.
[PDF]
arXiv:1909.04462
- Periods of Ducci sequences and odd solutions to a Pellian equation.
Bull. Aust. Math. Soc. 100 no.2 (2019), 201-205.
[PDF]
- On certain Drinfeld modular forms of higher rank. (with
Dirk Basson).
J. Théor. Nombres Bordeaux 29 no.3 (2017), 827-843.
[PDF]
- A note on Gekeler's h-function. Arch. Math. 107 (2016), 305-313. [PDF]
The final publication is available at Springer via
http://dx.doi.org/doi:10.1007/s00013-016-0923-1.
arXiv:1605.02567
- Drinfeld modular polynomials in higher rank II: Kronecker congruences.
(With
Hans-Georg Rück).
J. Number Theory 165 (2016), 1-14.
[PDF]
arXiv:1303.4086
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Explicit Drinfeld moduli schemes and Abhyankar's generalized iteration conjecture.
J. Number Theory 160 (2016), 432-450.
[PDF]
arXiv:1503.06420
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Newton identities for Weierstrass products.
Amer. Math. Monthly 119, no. 9 (2012), 796-799.
[PDF]
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Special subvarieties of Drinfeld modular varieties.
J. reine angew. Math. 668 (2012), 35-57.
[PDF]
arXiv:math/0503452
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Ducci sequences and cyclotomic fields.
J. Difference Equ. Appl. 16 (2010), no. 7, 847-862.
[PDF]
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Torsion bounds for elliptic curves and Drinfeld modules.
J. Number Theory 130 (2010), 1241-1250.
[PDF]
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Drinfeld modular polynomials in higher rank.
J. Number Theory 129 (2009), 59-83.
(With
Hans-Georg Rück)
[PDF]
arXiv:math/0701291
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Heegner points and the rank of elliptic curves over large extensions of global fields.
Canadian J. Math. 60 (2008), no.3, 481-490. (With Bo-Hae Im)
[PDF]
arXiv:math/0604107
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The André-Oort conjecture for Drinfeld modular varieties.
C. R. Math. Acad. Sci. Paris, Ser. I, 344 (2007), 733-736. [PDF]
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Ducci sequences in higher dimensions. Integers: Electronic Journal of Combinatorial
Number Theory 7 (2007), #A24.
[PDF]
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Ducci sequences and cyclotomic polynomials.
Finite Fields Appl. 13 (2007), 293-304.
(With Ernest Lötter and Brink van der Merwe.)
[PDF]
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CM points on products of Drinfeld modular curves.
Trans. Amer. Math. Soc.
359 (2007), 1351-1374.
[PDF]
arXiv:math/0407334
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Monodromy groups associated to non-isotrivial Drinfeld modules
in generic characteristic. In:
"Number Fields and Function Fields - Two Parallel Worlds",
(G. van der Geer, B. Moonen, R. Schoof, eds.),
Progress in Mathematics, 239,
p61-69,
Birkhäuser Verlag, 2005.
(With Richard Pink.)
[PDF]
arXiv:math/0407335
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The André-Oort conjecture for products of Drinfeld modular
curves.
J. reine angew. Math. 579 (2005), 115-144.
[PDF]
arXiv:math/0303038
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Images of isogeny classes on modular elliptic curves.
Math. Res. Lett. 11 (2004), 649-651.
[PDF]
arXiv:math/0407336
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Higher Heegner points on elliptic curves over function
fields. J. Number Theory 104 (2004), 315-326.
[PDF]
arXiv:math/0304216
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La conjecture d'André-Oort pour le produit de deux
coubres modulaires de Drinfeld. C. R. Math. Acad. Sci. Paris
335 (2002), no. 11, 867--870.
[PDF]
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Distinguished liftings and the André-Oort conjecture.
Quaest. Math. 25(3) (2002), 363-380.
[PDF]
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Heights of CM points on complex affine curves.
Ramanujan J. 5 (2001), 311-317.
[PDF]
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Ducci sequences over abelian groups.
Comm. Algebra 27.12 (1999), 5999-6013.
[PDF]
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A note on a paper by Glaser and Schöffl.
Fibonacci Quart. 36.5 (1998), 463-466.
[PDF]
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Strategy and complexity of the game of squares.
Bull. London. Math. Soc 30 (1998), 274-282.
(With Mike Robson)
[PDF]
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Line profile variations in the spectra of the gamma Dor star HR 2740,
In: IAU Symposium 185
"New Eyes to See Inside the Sun and Stars", (F.-L. Deubner, J. Christensen-Dalsgaard, D. Kurtz, eds) Kyoto, Japan, 18-22 August, 1997, p. 387.
(5th author, with E. Poretti, L. Mantegazza, C. Koen, P. Martinez,
D. De Alwis and H. Haupt).
[PDF]
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Discovery and analysis
of gamma doradus type pulsations in the F0 IV star HR 2740 QW pup,
Mon. Not. R. Astron. Soc. 292 (1997), 621-630.
(4th author, with E. Poretti, C. Koen, P. Martinez, D. de Alwis and H. Haupt)
[PDF]